Kontsevich invariant

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In the mathematical theory of knots, the Kontsevich invariant, also known as the Kontsevich integral[1] of an oriented framed link, is a universal Vassiliev invariant[2] in the sense that any coefficient of the Kontsevich invariant is of a finite type, and conversely any finite type invariant can be presented as a linear combination of such coefficients. It was defined by Maxim Kontsevich.

The Kontsevich invariant is a universal quantum invariant in the sense that any quantum invariant may be recovered by substituting the appropriate weight system into any Jacobi diagram.


The Kontsevich invariant is defined by monodromy along solutions of the Knizhnik–Zamolodchikov equations.


  1. ^ Chmutov, Sergei; Duzhi, Sergei (2012). Weisstein, Eric W, ed. "Kontsevich Integral". Mathworld (Wolfram Web Resource). Retrieved 4 December 2012. 
  2. ^ Kontsevich, Maxim (1993). "Vassiliev's knot invariants". Adv. Soviet Math 16 (2): 137.